pacman::p_load(sp, sf, raster, spatstat, tmap)Hands-on EX03: Spatial Point Pattern Analysis Methods
Loading libraries that are needed for this exercise
importing data that are needed for this analysis
childcare_sf <- st_read("data/geospatial/ChildCareServices.geojson") |>
st_transform(crs = 3414)Reading layer `ChildCareServices' from data source
`/Users/chuangjinlei/Desktop/JinLei13/IS415-GAA/Hands-on_Ex/Hands-on_Ex03/data/geospatial/ChildCareServices.geojson'
using driver `GeoJSON'
Simple feature collection with 1925 features and 2 fields
Geometry type: POINT
Dimension: XYZ
Bounding box: xmin: 103.6878 ymin: 1.247759 xmax: 103.9897 ymax: 1.462134
z_range: zmin: 0 zmax: 0
Geodetic CRS: WGS 84sg_sf <- st_read(dsn = "data/geospatial", layer="CostalOutline")Reading layer `CostalOutline' from data source
`/Users/chuangjinlei/Desktop/JinLei13/IS415-GAA/Hands-on_Ex/Hands-on_Ex03/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 60 features and 4 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 2663.926 ymin: 16357.98 xmax: 56047.79 ymax: 50244.03
Projected CRS: SVY21mpsz_sf <- st_read(dsn = "data/geospatial",
layer = "MP14_SUBZONE_WEB_PL")Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/chuangjinlei/Desktop/JinLei13/IS415-GAA/Hands-on_Ex/Hands-on_Ex03/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21Mapping of geospatial data sets
tmap_mode("plot")tmap mode set to plottingtm_shape(mpsz_sf) +
tm_polygons() +
tm_shape(childcare_sf) +
tm_dots()
Pin map of datasets
- ‘view’ option allows us to create an interactive map
tmap_mode('view')tmap mode set to interactive viewingtm_shape(childcare_sf)+
tm_dots()converting sf dataframe to sp’s spatial*class and displaying information of dataframes
- can be done using as_spatial() function
childcare <- as_Spatial(childcare_sf)
mpsz <- as_Spatial(mpsz_sf)
sg <- as_Spatial(sg_sf)
childcareclass : SpatialPointsDataFrame
features : 1925
extent : 11810.03, 45404.24, 25596.33, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 2
names : Name, Description
min values : kml_1, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>100044</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>44, TELOK BLANGAH DRIVE, #01 - 19/51, SINGAPORE 100044</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td></td> </tr><tr bgcolor=""> <th>NAME</th> <td>PCF SPARKLETOTS PRESCHOOL @ TELOK BLANGAH BLK 44 (CC)</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>349C54F201805938</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20211201093837</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center>
max values : kml_999, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>99982</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>35, ALLANBROOKE ROAD, SINGAPORE 099982</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td></td> </tr><tr bgcolor=""> <th>NAME</th> <td>ISLANDER PRE-SCHOOL PTE LTD</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>4F63ACF93EFABE7F</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20211201093837</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> mpszclass : SpatialPolygonsDataFrame
features : 323
extent : 2667.538, 56396.44, 15748.72, 50256.33 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m +no_defs
variables : 15
names : OBJECTID, SUBZONE_NO, SUBZONE_N, SUBZONE_C, CA_IND, PLN_AREA_N, PLN_AREA_C, REGION_N, REGION_C, INC_CRC, FMEL_UPD_D, X_ADDR, Y_ADDR, SHAPE_Leng, SHAPE_Area
min values : 1, 1, ADMIRALTY, AMSZ01, N, ANG MO KIO, AM, CENTRAL REGION, CR, 00F5E30B5C9B7AD8, 16409, 5092.8949, 19579.069, 871.554887798, 39437.9352703
max values : 323, 17, YUNNAN, YSSZ09, Y, YISHUN, YS, WEST REGION, WR, FFCCF172717C2EAF, 16409, 50424.7923, 49552.7904, 68083.9364708, 69748298.792 sgclass : SpatialPolygonsDataFrame
features : 60
extent : 2663.926, 56047.79, 16357.98, 50244.03 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m +no_defs
variables : 4
names : GDO_GID, MSLINK, MAPID, COSTAL_NAM
min values : 1, 1, 0, ISLAND LINK
max values : 60, 67, 0, SINGAPORE - MAIN ISLAND Converting the sp’s Spatial* class into generic sp format
childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")
childcare_spclass : SpatialPoints
features : 1925
extent : 11810.03, 45404.24, 25596.33, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs sg_spclass : SpatialPolygons
features : 60
extent : 2663.926, 56047.79, 16357.98, 50244.03 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m +no_defs converting the generic sf format into spatstat’s ppp format and plotting the data
library(dplyr)
Attaching package: 'dplyr'The following object is masked from 'package:nlme':
collapseThe following objects are masked from 'package:raster':
intersect, select, unionThe following objects are masked from 'package:stats':
filter, lagThe following objects are masked from 'package:base':
intersect, setdiff, setequal, unionchildcare_ppp <- childcare_sf$geometry |> as.ppp()
childcare_pppPlanar point pattern: 1925 points
window: rectangle = [11810.03, 45404.24] x [25596.33, 49300.88] unitstmap_mode('plot')tmap mode set to plottingplot(childcare_ppp)
summary(childcare_ppp)Planar point pattern: 1925 points
Average intensity 2.417323e-06 points per square unit
*Pattern contains duplicated points*
Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units
Window: rectangle = [11810.03, 45404.24] x [25596.33, 49300.88] units
(33590 x 23700 units)
Window area = 796335000 square unitsChecking for duplication
any(duplicated(childcare_ppp))[1] TRUEResult from the earlier analysis showed that there are duplication. Hence, we can use multiplicity () and sum() function to count how many locations have more than one point event
sum(multiplicity(childcare_ppp))[1] 2451Viewing locations of these duplicated point events
tmap_mode('view')tmap mode set to interactive viewingtm_shape(childcare) +
tm_dots(alpha=0.4,
size=0.05)Jittering approach which adds a small perturbation to the duplicated points so that they do not occupy the exact same space.
childcare_ppp_jit <- rjitter(childcare_ppp,
retry=TRUE,
nsim=1,
drop=TRUE)Checking for duplicated points again after performing jittering
any(duplicated(childcare_ppp_jit))[1] FALSECreating an owin object and plotting it
sg_owin <- as.owin(sg_sf)
plot(sg_owin)
summary(sg_owin)Window: polygonal boundary
50 separate polygons (1 hole)
vertices area relative.area
polygon 1 (hole) 30 -7081.18 -9.76e-06
polygon 2 55 82537.90 1.14e-04
polygon 3 90 415092.00 5.72e-04
polygon 4 49 16698.60 2.30e-05
polygon 5 38 24249.20 3.34e-05
polygon 6 976 23344700.00 3.22e-02
polygon 7 721 1927950.00 2.66e-03
polygon 8 1992 9992170.00 1.38e-02
polygon 9 330 1118960.00 1.54e-03
polygon 10 175 925904.00 1.28e-03
polygon 11 115 928394.00 1.28e-03
polygon 12 24 6352.39 8.76e-06
polygon 13 190 202489.00 2.79e-04
polygon 14 37 10170.50 1.40e-05
polygon 15 25 16622.70 2.29e-05
polygon 16 10 2145.07 2.96e-06
polygon 17 66 16184.10 2.23e-05
polygon 18 5195 636837000.00 8.78e-01
polygon 19 76 312332.00 4.31e-04
polygon 20 627 31891300.00 4.40e-02
polygon 21 20 32842.00 4.53e-05
polygon 22 42 55831.70 7.70e-05
polygon 23 67 1313540.00 1.81e-03
polygon 24 734 4690930.00 6.47e-03
polygon 25 16 3194.60 4.40e-06
polygon 26 15 4872.96 6.72e-06
polygon 27 15 4464.20 6.15e-06
polygon 28 14 5466.74 7.54e-06
polygon 29 37 5261.94 7.25e-06
polygon 30 111 662927.00 9.14e-04
polygon 31 69 56313.40 7.76e-05
polygon 32 143 145139.00 2.00e-04
polygon 33 397 2488210.00 3.43e-03
polygon 34 90 115991.00 1.60e-04
polygon 35 98 62682.90 8.64e-05
polygon 36 165 338736.00 4.67e-04
polygon 37 130 94046.50 1.30e-04
polygon 38 93 430642.00 5.94e-04
polygon 39 16 2010.46 2.77e-06
polygon 40 415 3253840.00 4.49e-03
polygon 41 30 10838.20 1.49e-05
polygon 42 53 34400.30 4.74e-05
polygon 43 26 8347.58 1.15e-05
polygon 44 74 58223.40 8.03e-05
polygon 45 327 2169210.00 2.99e-03
polygon 46 177 467446.00 6.44e-04
polygon 47 46 699702.00 9.65e-04
polygon 48 6 16841.00 2.32e-05
polygon 49 13 70087.30 9.66e-05
polygon 50 4 9459.63 1.30e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 725376000 square units
Fraction of frame area: 0.401Combining both point events object and owin object that have been create and plotting the result
childcareSG_ppp = childcare_ppp[sg_owin]
summary(childcareSG_ppp)Planar point pattern: 1925 points
Average intensity 2.653796e-06 points per square unit
*Pattern contains duplicated points*
Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units
Window: polygonal boundary
50 separate polygons (1 hole)
vertices area relative.area
polygon 1 (hole) 30 -7081.18 -9.76e-06
polygon 2 55 82537.90 1.14e-04
polygon 3 90 415092.00 5.72e-04
polygon 4 49 16698.60 2.30e-05
polygon 5 38 24249.20 3.34e-05
polygon 6 976 23344700.00 3.22e-02
polygon 7 721 1927950.00 2.66e-03
polygon 8 1992 9992170.00 1.38e-02
polygon 9 330 1118960.00 1.54e-03
polygon 10 175 925904.00 1.28e-03
polygon 11 115 928394.00 1.28e-03
polygon 12 24 6352.39 8.76e-06
polygon 13 190 202489.00 2.79e-04
polygon 14 37 10170.50 1.40e-05
polygon 15 25 16622.70 2.29e-05
polygon 16 10 2145.07 2.96e-06
polygon 17 66 16184.10 2.23e-05
polygon 18 5195 636837000.00 8.78e-01
polygon 19 76 312332.00 4.31e-04
polygon 20 627 31891300.00 4.40e-02
polygon 21 20 32842.00 4.53e-05
polygon 22 42 55831.70 7.70e-05
polygon 23 67 1313540.00 1.81e-03
polygon 24 734 4690930.00 6.47e-03
polygon 25 16 3194.60 4.40e-06
polygon 26 15 4872.96 6.72e-06
polygon 27 15 4464.20 6.15e-06
polygon 28 14 5466.74 7.54e-06
polygon 29 37 5261.94 7.25e-06
polygon 30 111 662927.00 9.14e-04
polygon 31 69 56313.40 7.76e-05
polygon 32 143 145139.00 2.00e-04
polygon 33 397 2488210.00 3.43e-03
polygon 34 90 115991.00 1.60e-04
polygon 35 98 62682.90 8.64e-05
polygon 36 165 338736.00 4.67e-04
polygon 37 130 94046.50 1.30e-04
polygon 38 93 430642.00 5.94e-04
polygon 39 16 2010.46 2.77e-06
polygon 40 415 3253840.00 4.49e-03
polygon 41 30 10838.20 1.49e-05
polygon 42 53 34400.30 4.74e-05
polygon 43 26 8347.58 1.15e-05
polygon 44 74 58223.40 8.03e-05
polygon 45 327 2169210.00 2.99e-03
polygon 46 177 467446.00 6.44e-04
polygon 47 46 699702.00 9.65e-04
polygon 48 6 16841.00 2.32e-05
polygon 49 13 70087.30 9.66e-05
polygon 50 4 9459.63 1.30e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 725376000 square units
Fraction of frame area: 0.401tmap_mode('plot')tmap mode set to plottingplot(childcareSG_ppp)
Computing kernel density estimation using automatic bandwidth selection method and plotting the result
kde_childcareSG_bw <- density(childcareSG_ppp,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian")
plot(kde_childcareSG_bw)
Retrieving the bandwidth used to compute the kde layer
bw <- bw.diggle(childcareSG_ppp)
bw sigma
306.6986 Rescaling the original unit of measurement from meters to kilometers
childcareSG_ppp.km <- rescale(childcareSG_ppp, 1000, "km")Re-running kernel density estimation after changing unit of measurement
kde_childcareSG.bw <- density(childcareSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG.bw)
Working with other bandwidth selection methods and the options are:
- bw.CvL()
- bw.scott()
- bw.ppl()
- bw.diggle()
bw.CvL(childcareSG_ppp.km) sigma
4.543278 bw.scott(childcareSG_ppp.km) sigma.x sigma.y
2.159749 1.396455 bw.ppl(childcareSG_ppp.km) sigma
0.3897114 bw.diggle(childcareSG_ppp.km) sigma
0.3066986 Comparing output of using different bandwidth selection method
kde_childcareSG.ppl <- density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="gaussian")
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "bw.diggle")
plot(kde_childcareSG.ppl, main = "bw.ppl")
Working with different kernel estimation methods
default: gaussian
- Epanechnikov
- Quartic
- Dics
par(mfrow=c(2,2))
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="gaussian"),
main="Gaussian")
plot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="epanechnikov"),
main="Epanechnikov")Warning in density.ppp(childcareSG_ppp.km, sigma = bw.ppl, edge = TRUE, :
Bandwidth selection will be based on Gaussian kernelplot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="quartic"),
main="Quartic")Warning in density.ppp(childcareSG_ppp.km, sigma = bw.ppl, edge = TRUE, :
Bandwidth selection will be based on Gaussian kernelplot(density(childcareSG_ppp.km,
sigma=bw.ppl,
edge=TRUE,
kernel="disc"),
main="Disc")Warning in density.ppp(childcareSG_ppp.km, sigma = bw.ppl, edge = TRUE, :
Bandwidth selection will be based on Gaussian kernel
Computing Kernel density estimation by using fixed bandwidth
kde_childcareSG_600 <- density(childcareSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG_600)
Computing Kernel Density Estimation by using adaptive bandwidth
kde_childcareSG_adaptive <- adaptive.density(childcareSG_ppp.km, method="kernel")
plot(kde_childcareSG_adaptive)
Plotting and comparing the output of using fixed and adaptive Kernel Density Estimation method
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "Fixed bandwidth")
plot(kde_childcareSG_adaptive, main = "Adaptive bandwidth")
Converting Kernel Density estimation into grid object for mapping purposes
gridded_kde_childcareSG_bw <- as(kde_childcareSG.bw, "SpatialGridDataFrame")
spplot(gridded_kde_childcareSG_bw)
Converting gridded output into raster
kde_childcareSG_bw_raster <- raster(gridded_kde_childcareSG_bw)
kde_childcareSG_bw_rasterclass : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348 (x, y)
extent : 2.663926, 56.04779, 16.35798, 50.24403 (xmin, xmax, ymin, ymax)
crs : NA
source : memory
names : v
values : -1.014191e-14, 32.45281 (min, max)Assigning projection system as NA was showed earlier on
projection(kde_childcareSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_childcareSG_bw_rasterclass : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348 (x, y)
extent : 2.663926, 56.04779, 16.35798, 50.24403 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs
source : memory
names : v
values : -1.014191e-14, 32.45281 (min, max)Visualising the output in tmap
tm_shape(kde_childcareSG_bw_raster) +
tm_raster("v") +
tm_layout(legend.position = c("right", "bottom"), frame = FALSE)Variable(s) "v" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
Extracting different study areas and plotting the target planning areas
pg = mpsz[mpsz@data$PLN_AREA_N == "PUNGGOL",]
tm = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]
ck = mpsz[mpsz@data$PLN_AREA_N == "CHOA CHU KANG",]
jw = mpsz[mpsz@data$PLN_AREA_N == "JURONG WEST",]
par(mfrow=c(2,2))
plot(pg, main = "Ponggol")
plot(tm, main = "Tampines")
plot(ck, main = "Choa Chu Kang")
plot(jw, main = "Jurong West")
Converting the spatial dataframe into generic sp format
pg_sp = as(pg, "SpatialPolygons")
tm_sp = as(tm, "SpatialPolygons")
ck_sp = as(ck, "SpatialPolygons")
jw_sp = as(jw, "SpatialPolygons")Creating an owin object
pg_owin = as.owin(mpsz_sf[mpsz@data$PLN_AREA_N == "PUNGGOL",])
tm_owin = as.owin(mpsz_sf[mpsz@data$PLN_AREA_N == "TAMPINES",])
ck_owin = as.owin(mpsz_sf[mpsz@data$PLN_AREA_N == "CHOA CHU KANG",])
jw_owin = as.owin(mpsz_sf[mpsz@data$PLN_AREA_N == "JURONG WEST",])Combining childcare points and the study area
childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]Changing unit of measurement from meters to kilometers
childcare_pg_ppp.km = rescale(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale(childcare_jw_ppp, 1000, "km")Plotting the four study areas and the location of childcares
par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")
plot(childcare_tm_ppp.km, main="Tampines")
plot(childcare_ck_ppp.km, main="Choa Chu Kang")
plot(childcare_jw_ppp.km, main="Jurong West")
Computing Kernel Density Estimation of the four study areas
par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Punggol")
plot(density(childcare_tm_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Tempines")
plot(density(childcare_ck_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="Choa Chu Kang")
plot(density(childcare_jw_ppp.km,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian"),
main="JUrong West")
Computing fixed bandwidth Kernel Density Estimation of the study areas
par(mfrow=c(2,2))
plot(density(childcare_ck_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Chou Chu Kang")
plot(density(childcare_jw_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="JUrong West")
plot(density(childcare_pg_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Punggol")
plot(density(childcare_tm_ppp.km,
sigma=0.25,
edge=TRUE,
kernel="gaussian"),
main="Tampines")
Testing spatial point patterns using Clark and Evans Test
- P-value is 0.01 < 0.05. Hence, we can reject the null hypothesis and infer that the distribution of childcare services are not randomly distributed
clarkevans.test(childcareSG_ppp,
correction="none",
clipregion="sg_owin",
alternative=c("clustered"),
nsim=99)
Clark-Evans test
No edge correction
Monte Carlo test based on 99 simulations of CSR with fixed n
data: childcareSG_ppp
R = 0.51429, p-value = 0.01
alternative hypothesis: clustered (R < 1)Conducting Clark and Evans Test on Choa Chu Kang planning area
- P-value is 0.024 < 0.05. Hence, we can reject the null hypothesis and infer that the distribution of childcare services in Choa Chu Kang are not randomly distributed
clarkevans.test(childcare_ck_ppp,
correction="none",
clipregion=NULL,
alternative=c("two.sided"),
nsim=999)
Clark-Evans test
No edge correction
Monte Carlo test based on 999 simulations of CSR with fixed n
data: childcare_ck_ppp
R = 0.86578, p-value = 0.004
alternative hypothesis: two-sidedConducting Clark and Evans Test on Tampines planning area
- P-value is 0.002 < 0.05. Hence, we can reject the null hypothesis and infer that the distribution of childcare services in Tampines are not randomly distributed
clarkevans.test(childcare_tm_ppp,
correction="none",
clipregion=NULL,
alternative=c("two.sided"),
nsim=999)
Clark-Evans test
No edge correction
Monte Carlo test based on 999 simulations of CSR with fixed n
data: childcare_tm_ppp
R = 0.69044, p-value = 0.002
alternative hypothesis: two-sidedComputing G-function estimation for Choa Chu Kang Planning area
G_CK = Gest(childcare_ck_ppp, correction = "border")
plot(G_CK, xlim=c(0,500))
Performing Complete Spatial Randomness Test for hypothesis testing
G_CK.csr <- envelope(childcare_ck_ppp, Gest, nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.
Done.plot(G_CK.csr)
Computing G-function estimation for Tampines planning area
G_tm = Gest(childcare_tm_ppp, correction = "best")
plot(G_tm)
Performing Complete Spatial Randomness Test for hypothesis in Tampines planning area
G_tm.csr <- envelope(childcare_tm_ppp, Gest, correction = "all", nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.
Done.plot(G_tm.csr)
Computing F-function estimation for Choa Chu Kang planning area
F_CK = Fest(childcare_ck_ppp)
plot(F_CK)
Performing Complete Spatial Randomness test for hypothesis testing in Choa Chu Kang Planning area
F_CK.csr <- envelope(childcare_ck_ppp, Fest, nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.
Done.plot(F_CK.csr)
Computing F-function estimation for Tampines planning area
F_tm = Fest(childcare_tm_ppp, correction = "best")
plot(F_tm)
Performing Complete Spatial Randomness test for hypothesis testing in Tampines planning area
F_tm.csr <- envelope(childcare_tm_ppp, Fest, correction = "all", nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.
Done.plot(F_tm.csr)
Computing K-function estimation for Choa Chu Kang Planning area
K_ck = Kest(childcare_ck_ppp, correction = "Ripley")
plot(K_ck, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")
Performing Complete Spatial Randomness Test for hypothesis testing in Choa Chu Kang planning area
K_ck.csr <- envelope(childcare_ck_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.
Done.plot(K_ck.csr, . - r ~ r, xlab="d", ylab="K(d)-r")
Computing K-function estimation for Tampines planning area
K_tm = Kest(childcare_tm_ppp, correction = "Ripley")
plot(K_tm, . -r ~ r,
ylab= "K(d)-r", xlab = "d(m)",
xlim=c(0,1000))
Performing Complete Spatial Randomness Test for hypothesis testing for Tampines planning area
K_tm.csr <- envelope(childcare_tm_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.
Done.plot(K_tm.csr, . - r ~ r,
xlab="d", ylab="K(d)-r", xlim=c(0,500))
Computing L-function estimation for Choa Chu Kang planning area
L_ck = Lest(childcare_ck_ppp, correction = "Ripley")
plot(L_ck, . -r ~ r,
ylab= "L(d)-r", xlab = "d(m)")
Performing Complete Spatial Randomness Test for hypothesis testing for Choa Chu Kang planning area
L_ck.csr <- envelope(childcare_ck_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.
Done.plot(L_ck.csr, . - r ~ r, xlab="d", ylab="L(d)-r")
Computing L-function estimation for Tampines planning area
L_tm = Lest(childcare_tm_ppp, correction = "Ripley")
plot(L_tm, . -r ~ r,
ylab= "L(d)-r", xlab = "d(m)",
xlim=c(0,1000))
Performing Complete Spatial Randomness Test for hypothesis testing in Tampines planning area
L_tm.csr <- envelope(childcare_tm_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.
Done.plot(L_tm.csr, . - r ~ r,
xlab="d", ylab="L(d)-r", xlim=c(0,500))